Correlation analysis
Matt Blanchard
14/05/2019
First, let’s look at the relationship between accuracy variables
## adr.ind.acc crt.ind.acc gk.ind.accO gk.ind.accR gk.ind.accUR mdmt.ind.acc rapm.ind.acc
## adr.grp.acc 0.89 0.42 0.35 0.31 0.23 0.35 0.44
## crt.grp.acc 0.53 0.89 0.21 0.23 0.41 0.53
## gk.grp.accO 0.79 0.59 0.64
## gk.grp.accR 0.54 0.74
## gk.grp.accUR 0.6 0.77
## mdmt.grp.acc 0.38 0.34 0.48 0.39
## rapm.grp.acc 0.46 0.56 0.47 0.78Within the same test, we can see that individual and group accuracy (diagonal in correlation matrix) is strongly and positively correlated for all tests.
In the correlation plot two clusters are evident:
- The cluster in the top left corner is a positive manifold between accuracy varaibles on ADR, CRT, MDMT and RAPM form. Individuals and dyads that perform well on one of these tests tend to perform well on the other tests.
- The second cluster in the bottom right corner contains only the general-knowledge test accuracy varaibles. Performance on this test is not related to performance on the other tests.
Next, let’s check out the confidence variables
## adr.ind.conf crt.ind.conf gk.ind.confO gk.ind.confR gk.ind.confUR mdmt.ind.conf rapm.ind.conf
## adr.grp.conf 0.93 0.63 0.48 0.51 0.43 0.38 0.53
## crt.grp.conf 0.75 0.81 0.48 0.51 0.43 0.45 0.63
## gk.grp.confO 0.48 0.40 0.93 0.89 0.91 0.28 0.23
## gk.grp.confR 0.50 0.44 0.91 0.90 0.86 0.31 0.26
## gk.grp.confUR 0.44 0.33 0.90 0.84 0.92 0.23 0.19
## mdmt.grp.conf 0.59 0.49 0.37 0.39 0.33 0.57 0.55
## rapm.grp.conf 0.63 0.59 0.38 0.39 0.35 0.50 0.77Within the same test, we can see that individual and group confidence (diagonal in correlation matrix) is strongly and positively correlated for all tests.
There is a positive manifold between all confidence variables. Indicating that higher confidence on one test tends to be associated with higher confidence on the other tests.
Do accuracy and confidence correlate?
## adr.ind.acc crt.ind.acc gk.ind.accO gk.ind.accR gk.ind.accUR mdmt.ind.acc rapm.ind.acc adr.grp.acc crt.grp.acc gk.grp.accO gk.grp.accR gk.grp.accUR mdmt.grp.acc rapm.grp.acc
## adr.ind.conf 0.38 0.45 0.29 0.28 0.39 0.45 0.35
## crt.ind.conf 0.25 0.55 0.24 0.32 0.26 0.46 0.36
## gk.ind.confO 0.22
## gk.ind.confR 0.25
## gk.ind.confUR
## mdmt.ind.conf 0.23 0.37 0.71 0.4 0.29 0.34 0.3 0.41
## rapm.ind.conf 0.34 0.5 0.5 0.63 0.35 0.5 0.28 0.61
## adr.grp.conf 0.41 0.39 0.24 0.21 0.23 0.24 0.45 0.39 0.21 0.32
## crt.grp.conf 0.37 0.61 0.34 0.44 0.38 0.61 0.23 0.42
## gk.grp.confO 0.21 0.23
## gk.grp.confR 0.23 0.28
## gk.grp.confUR
## mdmt.grp.conf 0.22 0.36 0.36 0.36 0.29 0.36 0.38 0.36
## rapm.grp.conf 0.26 0.43 0.41 0.55 0.29 0.4 0.23 0.64Within the same test, we can see that accuracy and confidence (diagonal in correlation matrix) is moderately and positively correlated for all tests except GK.
There is a positive manifold between all accuracy and confidence variables except the general-knowledge test. Indicating that participants with higher confidence tend to have higher accuracy on all tests except GK.
What about the POST variables?
## adr.ind.post crt.ind.post gk.ind.postO gk.ind.postR gk.ind.postUR mdmt.ind.post rapm.ind.post
## adr.grp.post 0.64 0.35 0.41 0.27 0.38 0.2
## crt.grp.post 0.31 0.4 0.5 0.46 0.36 0.45
## gk.grp.postO 0.62 0.49 0.43 0.25 0.32
## gk.grp.postR 0.38 0.66 0.63 0.52 0.4
## gk.grp.postUR 0.47 0.36 0.42 0.32
## mdmt.grp.post
## rapm.grp.post 0.42 0.22 0.46 0.42 0.39 0.48Within the same test, we can see that individual and group POSTs (diagonal in correlation matrix) are moderately and positively correlated for all tests except MDMT.
With the exception of MDMT, there appears to be a positive manifold between POST variables. Indicating that higher POST scores on one test tend to be associated with higher POST scores on the other tests.
How does POST relate to accuracy and confidence?
## adr.ind.post crt.ind.post gk.ind.postO gk.ind.postR gk.ind.postUR mdmt.ind.post rapm.ind.post adr.grp.post crt.grp.post gk.grp.postO gk.grp.postR gk.grp.postUR mdmt.grp.post rapm.grp.post
## adr.ind.acc
## crt.ind.acc 0.2
## gk.ind.accO 0.45
## gk.ind.accR 0.2
## gk.ind.accUR 0.21 0.2 0.52
## mdmt.ind.acc 0.2
## rapm.ind.acc 0.22
## adr.grp.acc
## crt.grp.acc
## gk.grp.accO 0.23 0.44
## gk.grp.accR
## gk.grp.accUR 0.25 0.55
## mdmt.grp.acc -0.24
## rapm.grp.acc 0.25 0.2 0.2 0.25
## adr.ind.conf 0.45 0.25 0.23 0.31 0.44 0.27 0.31 0.2
## crt.ind.conf 0.24 0.31 0.2 0.24 0.23 0.28
## gk.ind.confO 0.29 0.28 0.23 0.28 0.21
## gk.ind.confR 0.28 0.23 0.23 0.24
## gk.ind.confUR 0.28 0.21 0.31 0.28 0.32 0.23
## mdmt.ind.conf 0.27 0.46 0.31 0.2 0.31 0.32
## rapm.ind.conf 0.38 0.22 0.38 0.22 0.26 0.23
## adr.grp.conf 0.39 0.21 0.2 0.27 0.54 0.34 0.35 0.33
## crt.grp.conf 0.28 0.2 0.25 0.21 0.43 0.31 0.29
## gk.grp.confO 0.32 0.21 0.2 0.25 0.32
## gk.grp.confR 0.32 0.2 0.24 0.36
## gk.grp.confUR 0.3 0.27 0.24 0.21 0.26
## mdmt.grp.conf 0.34 0.36 0.21 0.2 0.31 0.51
## rapm.grp.conf 0.38 0.22 0.27 0.23 0.24 0.21 0.27 0.45 0.2Within the same test, we can see that individual and group POSTs (diagonal in correlation matrix) are moderately and positively correlated with confidence for all tests except GK individual responses. There is no relationship between POST and accuracy.
A number of clusters have formed: * confidence variables (top left) * POST variables (along the diagonal below the confidence cluster) * a weaker cluster containing confidence and POST varibles * GK accuracy (along the diagonal below the POST cluster) * accuracy on the other tests (along the diagonal below the GK accuracy cluster)
Let’s take a look at the DPA variables
Decisiveness
## adr.ind.dec crt.ind.dec gk.ind.decO gk.ind.decR gk.ind.decUR mdmt.ind.dec rapm.ind.dec
## adr.grp.dec 0.75 0.52 0.43 0.43 0.4
## crt.grp.dec 0.6 0.74 0.36 0.34 0.37 0.4
## gk.grp.decO 0.5 0.48 0.88 0.83 0.86
## gk.grp.decR 0.49 0.48 0.84 0.83 0.8
## gk.grp.decUR 0.47 0.44 0.84 0.77 0.85
## mdmt.grp.dec 0.31
## rapm.grp.dec 0.55 0.55 0.38 0.37 0.35 0.32 0.56Within the same test, we can see that individual and group decisiveness (diagonal in correlation matrix) are moderately and positively correlated for all tests.
With the exception of MDMT, there appears to be a positive manifold between the decisiveness variables. It is worth noting that RAPM correlates more weakly with GK tests. This pattern indicates that higher decisiveness on one test tends to be associated with higher decisiveness scores on the other tests.
Recklessness
## adr.ind.rec crt.ind.rec gk.ind.recO gk.ind.recR gk.ind.recUR mdmt.ind.rec rapm.ind.rec
## adr.grp.rec 0.6 0.3 0.26 0.27
## crt.grp.rec 0.44 0.49 0.30 0.34 0.21
## gk.grp.recO 0.35 0.42 0.79 0.73 0.71
## gk.grp.recR 0.29 0.34 0.67 0.69 0.57
## gk.grp.recUR 0.31 0.42 0.73 0.64 0.68
## mdmt.grp.rec -0.20 -0.22
## rapm.grp.rec 0.21 0.22 0.22Within the same test, we can see that individual and group recklessness (diagonal in correlation matrix) are moderately and positively correlated for ADR, CRT and GK but not for MDMT or RAPM.
There is a positive manifold between the recklessness variables for ADR, CRT and GK. This pattern indicates that higher recklessness on one of these tests tends to be associated with higher recklessness scores on the other tests. Recklessness on MDMT and RAPM does not correlate significantly with any of the other tests or each other.
Optimality
## adr.ind.optim crt.ind.optim gk.ind.optimO gk.ind.optimR gk.ind.optimUR mdmt.ind.optim rapm.ind.optim
## adr.grp.optim 0.85 0.5 0.31 0.29 0.29 0.36 0.37
## crt.grp.optim 0.59 0.87 0.29 0.23 0.31 0.39 0.56
## gk.grp.optimO 0.29 0.25 0.85 0.76 0.81
## gk.grp.optimR 0.27 0.31 0.82 0.82 0.69
## gk.grp.optimUR 0.26 0.7 0.55 0.77
## mdmt.grp.optim 0.40 0.34 0.45 0.35
## rapm.grp.optim 0.54 0.59 0.31 0.28 0.3 0.46 0.71Within the same test, we can see that individual and group optimality (diagonal in correlation matrix) are strongly and positively correlated for all tests.
There is a positive manifold between the optimality variables. With two caveats: 1) optimality on MDMT does not relate with GK and 2) ADR, CRT, RAPM correltates strongly with each other but weakly (and significantly) with GK. This pattern indicates that higher optimality on one test tends to be associated with higher optimality on the other tests.
Competence
## adr.ind.comp crt.ind.comp gk.ind.compO gk.ind.compR gk.ind.compUR mdmt.ind.comp rapm.ind.comp
## adr.grp.comp 0.7 0.39 0.25 0.26 0.26
## crt.grp.comp 0.48 0.57 0.22 0.25 0.23
## gk.grp.compO 0.2 0.52 0.38 0.38
## gk.grp.compR 0.48 0.53
## gk.grp.compUR 0.34 0.42
## mdmt.grp.comp 0.34 0.24
## rapm.grp.comp 0.34 0.23 0.34 0.3 0.32 0.43Within the same test, we can see that individual and group competence (diagonal in correlation matrix) is moderately and positively correlated for all tests.
There is a positive manifold between the optimality variables. With two caveats: 1) optimality on MDMT does not relate with GK and 2) ADR, CRT, RAPM correltates strongly with each other but weakly (and significantly) with GK. This pattern indicates that higher optimality on one test tends to be associated with higher optimality on the other tests.
Hesitancy
## adr.ind.hes crt.ind.hes gk.ind.hesO gk.ind.hesR gk.ind.hesUR mdmt.ind.hes rapm.ind.hes
## adr.grp.hes 0.65 0.29 0.45 0.44 0.42 0.23
## crt.grp.hes 0.41 0.47 0.27 0.22 0.26 0.22 0.35
## gk.grp.hesO 0.43 0.29 0.82 0.76 0.78
## gk.grp.hesR 0.41 0.25 0.76 0.74 0.69
## gk.grp.hesUR 0.4 0.3 0.74 0.65 0.75
## mdmt.grp.hes 0.22
## rapm.grp.hes 0.54 0.36 0.44 0.39 0.45 0.2 0.45Within the same test, we can see that individual and group hesitancy (diagonal in correlation matrix) is moderately and positively correlated for all tests.
There is a positive manifold between the hesitancy variables with a caveat: hesitancy on MDMT weakly relates to hesitancy on RAPM and CRT but nothing else. This pattern indicates that higher hesitancy on one test tends to be associated with higher hesitancy on the other tests.
Now let’s take a look at the relationships between our test variables and demographics
Proportion of females and accuracy, confidence and POST
## prop.female
## gk.ind.confR -0.44
## gk.ind.confO -0.43
## gk.grp.confR -0.40
## gk.ind.confUR -0.40
## crt.ind.conf -0.38
## crt.grp.conf -0.36
## gk.grp.confO -0.36
## adr.ind.conf -0.30
## crt.grp.acc -0.30
## gk.grp.confUR -0.29
## crt.ind.acc -0.29
## mdmt.ind.conf -0.28
## crt.grp.post -0.28
## adr.grp.conf -0.27
## rapm.grp.conf -0.24
## gk.ind.accR -0.22
## crt.ind.post -0.22
## mdmt.grp.conf -0.20
## mdmt.ind.post -0.20
## rapm.ind.conf -0.20
## adr.ind.acc -0.17
## adr.grp.acc -0.15
## gk.grp.postR -0.14
## rapm.grp.acc -0.13
## gk.grp.accR -0.11
## mdmt.ind.acc -0.10
## gk.ind.accO -0.09
## mdmt.grp.post -0.09
## mdmt.grp.acc -0.08
## gk.grp.postUR -0.08
## rapm.ind.post -0.08
## gk.ind.accUR 0.07
## rapm.ind.acc -0.04
## adr.ind.post -0.04
## gk.grp.accUR 0.04
## gk.grp.accO -0.04
## gk.grp.postO -0.02
## adr.grp.post -0.02
## gk.ind.postUR -0.01
## gk.ind.postO -0.01
## gk.ind.postR 0.01
## rapm.grp.post 0.00
There is a consistent pattern of small to moderate significant negative correlations between the confidence variables and the proportion of females in a group. For CRT, accuracy and POST are also significantly negatively correlated with the proportion of females.
## prop.female
## adr.ind.dec -0.26
## crt.ind.dec -0.36
## gk.ind.decO -0.40
## gk.ind.decR -0.40
## gk.ind.decUR -0.38
## mdmt.ind.dec -0.17
## rapm.ind.dec -0.10
## adr.grp.dec -0.20
## crt.grp.dec -0.22
## gk.grp.decO -0.32
## gk.grp.decR -0.33
## gk.grp.decUR -0.29
## mdmt.grp.dec -0.04
## rapm.grp.dec -0.25
## adr.ind.rec -0.11
## crt.ind.rec -0.29
## gk.ind.recO -0.34
## gk.ind.recR -0.28
## gk.ind.recUR -0.33
## mdmt.ind.rec -0.30
## rapm.ind.rec -0.03
## adr.grp.rec -0.06
## crt.grp.rec -0.06
## gk.grp.recO -0.20
## gk.grp.recR -0.14
## gk.grp.recUR -0.18
## mdmt.grp.rec 0.05
## rapm.grp.rec -0.06
## adr.ind.optim -0.29
## crt.ind.optim -0.37
## gk.ind.optimO -0.42
## gk.ind.optimR -0.43
## gk.ind.optimUR -0.33
## mdmt.ind.optim -0.12
## rapm.ind.optim -0.08
## adr.grp.optim -0.20
## crt.grp.optim -0.30
## gk.grp.optimO -0.27
## gk.grp.optimR -0.33
## gk.grp.optimUR -0.16
## mdmt.grp.optim -0.10
## rapm.grp.optim -0.24
## adr.ind.comp -0.22
## crt.ind.comp -0.11
## gk.ind.compO -0.28
## gk.ind.compR -0.31
## gk.ind.compUR -0.09
## mdmt.ind.comp 0.02
## rapm.ind.comp -0.05
## adr.grp.comp -0.15
## crt.grp.comp -0.21
## gk.grp.compO -0.10
## gk.grp.compR -0.24
## gk.grp.compUR 0.06
## mdmt.grp.comp -0.11
## rapm.grp.comp -0.23
## adr.ind.hes 0.29
## crt.ind.hes 0.27
## gk.ind.hesO 0.43
## gk.ind.hesR 0.42
## gk.ind.hesUR 0.38
## mdmt.ind.hes 0.10
## rapm.ind.hes 0.05
## adr.grp.hes 0.19
## crt.grp.hes 0.19
## gk.grp.hesO 0.35
## gk.grp.hesR 0.34
## gk.grp.hesUR 0.28
## mdmt.grp.hes 0.09
## rapm.grp.hes 0.23
There is a consistent pattern of small to moderate significant positive correlations between the hesitancy variables and the proportion of females in a group. There is also a consistent pattern of small to moderate significant negative correlations between the decisiveness and optimality variables and the proportion of females. Correlations with recklessness and competence are mixed.
